Name
Title | ||
|---|---|---|
High dimensional covariance matrix estimation by penalizing the matrix-logarithm transformed likelihood. |
Abstract | ||
|---|---|---|
It is well known that when the dimension of the data becomes very large, the sample covariance matrix S will not be a good estimator of the population covariance matrix Σ. Using such estimator, one typical consequence is that the estimated eigenvalues from S will be distorted. Many existing methods tried to solve the problem, and examples of which include regularizing Σ by thresholding or banding. In this paper, we estimate Σ by maximizing the likelihood using a new penalization on the matrix logarithm of Σ (denoted by A) of the form: ‖A−mI‖F2=∑i(log(di)−m)2, where di is the ith eigenvalue of Σ. This penalty aims at shrinking the estimated eigenvalues of A toward the mean eigenvalue m. The merits of our method are that it guarantees Σ to be non-negative definite and is computational efficient. The simulation study and applications on portfolio optimization and classification of genomic data show that the proposed method outperforms existing methods. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.csda.2017.04.004 | Computational Statistics & Data Analysis |
Keywords | Field | DocType |
Covariance matrix estimation,Matrix-logarithm transformation,Penalization | Econometrics,Population,Estimation of covariance matrices,Portfolio optimization,Thresholding,Covariance matrix,Logarithm of a matrix,Statistics,Eigenvalues and eigenvectors,Mathematics,Estimator | Journal |
Volume | ISSN | Citations |
114 | 0167-9473 | 0 |
PageRank | References | Authors |
0.34 | 1 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Philip L H Yu | 1 | 105 | 16.34 |
| Xiaohang Wang | 2 | 895 | 53.93 |
| Yuanyuan Zhu | 3 | 0 | 1.35 |